Here's an apparently sensible example where predict(backSpline(interSpline())) gives crazy answers. Greg Snow contributes a diagnosis, and I contribute a simpleminded patch based on one of his solutions. Someone with more knowledge and understanding of the context may well be able to do better ...
## original example
r2 <- c(1.04409027570601, 1.09953936543359, 1.15498845516117, 1.21043754488875,
1.26588663461633, 1.32133572434391, 1.37678481407149, 1.43223390379907,
1.48768299352664, 1.54313208325422, 1.5985811729818, 1.65403026270938,
1.70947935243696, 1.76492844216454, 1.82037753189212, 1.87582662161970,
1.93127571134727, 1.98672480107485, 2.04217389080243, 2.09762298053001
)
d2 <- c(6.1610616585333, 5.70079375491741, 5.2366151167289, 4.77263065800071,
4.31310259797181, 3.86232922249189, 3.42452047126494, 3.00367670365119,
2.6034766331926, 2.22717964214416, 1.87754657382891, 1.55678176465949,
1.26649764837839, 1.00770187223770, 0.780805622450771, 0.585650849661306,
0.421553364080296, 0.287358347766713, 0.18150469048976, 0.102094654969619
)
plot(d2,r2,type="b")
require(splines)
sp <- interpSpline(r2,d2)
psp <- predict(sp)
points(psp$y,psp$x,col=5)
bsp <- backSpline(sp)
lines(predict(bsp,seq(0,6,length=51)),col=2,type="b")
## Greg Snow says:
## I am pretty sure that you have found a bug, I am just not sure where exactly the bug would be.
## The problem comes from the fact that your bsp object has the knots
## in decreasing order, if we reverse the order like this:
bsp3 <- bsp
bsp3$knots <- rev(bsp$knots)
bsp3$coefficients <- bsp$coefficients[20:1,]
lines(predict(bsp3,seq(0,6,length=101)), col='blue')
## Then the prediction looks like it should.
## If we trace through the predict.polySpline function with x=5.6 as
## one example, then inside the prediction function the value of i
## (the interval between knots that x belongs to) is 18, well if the
## knots are in increasing order then that is the correct interval,
## this comes from the line: i <- as.numeric(cut(x, knots)) and the
## cut function treats the knots as being in increasing order, not
## decreasing, so that in a later step when the function is supposed
## to be finding how far x is from the closest knot below it (which
## should be 5.2366151 for your example) it grabs the 18 element of
## knots, which in its decending order is instead: 0.2873583, so the
## difference ends up being much too big, when the function squares
## and cubes this much too big value, we get values that are way off
## (as you noticed), the wrong set of coefficients is being used as
## well (also row 18, which correspond to 0.28 not 5.23). I would say
## that the most surprising thing with your example is the range at
## which the prediction is actually decent, I would only expect this
## between the middle 2 knots.
## I see 2 possible ways to fix the problem:
## 1. The predict function checks the order of the knots and either
## reorders the knots and coefficients when the knots are descending,
## or does the correct computations of the interval.
## 2. The backSpline function checks and makes sure that it always
## produces the results with the knots in ascending order (and the
## coefficients to match).
===================================================================
--- splineClasses.R (revision 52966)
+++ splineClasses.R (working copy)
@@ -568,7 +568,7 @@
bcoeff[nkm1, 3L] <- 0
bcoeff[nkm1, 2L] <- kdiff[nkm1]/adiff[nkm1]
}
- value <- list(knots = bknots, coefficients = bcoeff)
+ value <- list(knots = bknots[order(bknots)], coefficients = bcoeff[order(bknots),])
attr(value, "formula") <- do.call("~", as.list(attr(object, "formula"))[3L:2L])
class(value) <- c("polySpline", "spline")
value